Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
The series
S
=
∑
n
=
1
∞
(
−
1
)
n
+
1
1
n
S=\displaystyle\sum_{n=1}^{\infty}(-1)^{\,n+1}\dfrac{1}{n}
S
=
n
=
1
∑
∞
(
−
1
)
n
+
1
n
1
is approximated by
S
4
S_{4}
S
4
. Determine whether
S
4
S_{4}
S
4
is guaranteed to approximate
S
S
S
with absolute error no greater than
1
800
\dfrac{1}{800}
800
1
. Support your conclusion with a numerical bound.
Browse the problem library